This Review Article provides an overview of chaos in laser diodes by surveying experimental achievements in the area and explaining the theory behind the phenomenon. The fundamental physics underpinning laser diode chaos and also the opportunities for harnessing it for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient testbed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.

Physics and applications of laser diode chaos

This paper reports the experimental investigation of two different approaches to random bit generation based on the chaotic dynamics of a semiconductor laser with optical feedback. By computing high-order finite differences of the chaotic laser intensity time series, we obtain time series with symmetric statistical distributions that are more conducive to ultrafast random bit generation. The first approach is guided by information-theoretic considerations and could potentially reach random bit generation rates as high as 160 Gb/s by extracting 4 bits per sample. The second approach is based on pragmatic considerations and could lead to rates of 2.2 Tb/s by extracting 55 bits per sample. The randomness of the bit sequences obtained from the two approaches is tested against three standard randomness tests (ENT, Diehard, and NIST tests), as well as by calculating the statistical bias and the serial correlation coefficients on longer sequences of random bits than those used in the standard tests.

Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser

A semiconductor laser with delayed optical feedback is an experimental implementation of a nominally infinite dimensional dynamical system. As such, time series analysis of the output power from this laser system is an excellent test of complexity analysis tools, as applied to experimental data. Additionally, the systematic characterization of the range and variation in complexity that can be obtained in the output power from the system, which is available to be used in applications like secure communication, is of interest. Output power time series from a semiconductor laser system, as a function of the optical feedback level and the laser injection current, have been analyzed for complexity using permutation entropy. High resolution maps of permutation entropy as a function of optical feedback level and injection current have been achieved for the first time. This confirms prior research that identifies a coherence collapse region which is found to be uninterrupted with respect to any embedded islands with different dynamics. The results also show new observations of low optical feedback dynamics which occur in a region below that for coherence collapse. The map of the complexity shows a strong dependence on the delay time used in the permutation entropy calculation. Short delay times, which sample information at the complete measurement bandwidth, produce maps with drastically different systematic variation in complexity throughout the coherence collapse region, compared to maps generated with a delay time that matches the optical feedback delay. Evaluating the complexity with a permutation entropy delay equal to the external cavity delay produces results consistent with the notion of weak/strong chaos, as well as categorizing the dynamics as being of high complexity where the external cavity delay time is harder to identify. These are both desirable features for secure communication applications. The results also show permutation entropy as a function of delay time can be used to detect key frequencies driving the dynamics, including any that may exist due to, or arise from, technicalities of device fabrication and/or noise. A more complete insight into complexity as measured by permutation entropy is gained by considering multiple delay times.

Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy

Chaotic dynamics of a semiconductor laser subject to optical feedback from a frequency-detuned fiber Bragg grating (FBG) is investigated experimentally and numerically. Although the FBG is similar to a mirror in perturbing the laser into chaos, it is not the same as a mirror because it provides spatially distributed reflections. Such distributed reflections effectively suppress the undesirable time-delay signature (TDS) contained in the autocorrelation function of the chaotic intensity time-series. The investigation shows that the best suppression of TDS is attained when the FBG is positively detuned from the free-running laser frequency. The TDS suppression is due to dispersion at frequencies near an edge of the main lobe of the FBG reflectivity spectrum. The suppression prefers the FBG at a positive detuning frequency because the laser cavity is red-shifted by the antiguidance effect. Numerically, the dynamical behavior is mapped in the parameter space of detuning frequency and feedback strength, where wide regions of chaos are identified. Experimentally, the TDS suppression by FBG feedback is demonstrated for the first time. The positively detuned FBG suppresses the TDS by over ten times to below 0.04 in the experiments.

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Chaotic Time-Delay Signature Suppression in a Semiconductor Laser With Frequency-Detuned Grating Feedback

Both the time-delay signature and the bandwidth of chaos have been investigated in four schemes of chaos generation in vertical-cavity surface-emitting lasers (VCSELs). The results show that suppression of the TD signature and the enhanced bandwidth of chaos can be obtained simultaneously in two schemes - a chaotic beam unidirectionally injected into a CW VCSEL and a CW VCSEL mutually coupled to a chaotic VCSEL. However, suppression of the TD signature and the enhanced chaos bandwidth cannot be achieved simultaneously in two other schemes - a CW optical beam unidirectionally injected into a chaotic VCSEL and two mutually coupled CW VCSELs.

Wideband Chaos With Time-Delay Concealment in Vertical-Cavity Surface-Emitting Lasers With Optical Feedback and Injection

Time-delay (TD) signature concealment in a chaotic vertical-cavity surface-emitting laser (VCSEL) is studied experimentally. The VCSEL is subject to variable optical polarization angle of feedback along with variable optical feedback strength and bias current. The TD signature concealment is determined through the use of autocorrelation and information theory-based permutation entropy functions. It is found that the TD signature is concealed at low feedback of strength of order -18 dB. At moderate feedback strength, the TD signature is sensitive to the rotation of optical polarization angle of feedback with TD concealment being observed for polarization angles in the range from 45° to 90°.

Experimental Investigations of Time-Delay Signature Concealment in Chaotic External Cavity VCSELs Subject to Variable Optical Polarization Angle of Feedback

Thermal effects and dynamical hysteresis in VCSELs under dc modulation have been experimentally studied. The results show that the VCSEL turn-on and turn-off currents can display both positive hysteresis and negative hysteresis, depending on the current modulation frequency and on the substrate temperature. Numerical simulations of semiconductor laser rate equations, extended to take into account thermal effects, show a good agreement with the observations.

/pdf/thermal-effects-and-dynamical-hysteresis-in-the-turn-on-and-1najxoy1rn.pdf

Thermal effects and dynamical hysteresis in the turn-on and turn-off of vertical-cavity surface-emitting lasers

In optical chaos communications a message is masked in the noise-like broadband output of a chaotic transmitter laser, and message recovery is enabled through the synchronization of the transmitter and the (chaotic) receiver laser. Key issues are to identify the laser operating conditions which provide the highest quality synchronization conditions and those which provide optimized message extraction. In general such operating conditions are not coincident. In this paper numerical simulations are performed with the aim of identifying a regime of operation where the highest quality synchronization and optimizing message extraction efficiency are achieved simultaneously. Use of such an operating regime will facilitate practical deployment of optical chaos communications systems without the need for re-adjustment of laser operating conditions in the field.

https://iopscience.iop.org/article/10.1088/0268-1242/27/9/094002/pdf

Optimal operating conditions for external cavity semiconductor laser optical chaos communication system

The conductivity and permittivity of biological tissue are critical to estimating local radiofrequency (RF) power deposition (also known as specific absorption rate SAR) for Ultra High Field Magnetic Resonance Imaging (UH-MRI). These electrical properties may also have diagnostic value as malignant tissue types have been shown to have higher permittivity and conductivity than surrounding healthy tissue [1]. Recently a new SAR calculation method of using the transmit B 1 + map to obtain tissue electrical property has been proposed as a fast SAR calculation method, and has demonstrated great potential for practical applications. However the current numerical technique used in the B 1 + map based electrical property calculation is based on a traditional Finite-Difference algorithm, and therefore it requires high-resolution original B 1 + map to achieve accurate electrical property calculation. In this study, we have proposed the Spline interpolation of low resolution MRI B 1 + map at 1.5T. The proposed method is robust in approximating complex shapes in medical images through curve fitting and therefore could provide sufficiently accurate approximation of the high resolution B 1 + map through the low resolution raw data. This will prove to be useful in the fast real time estimation of local specific absorption rate without compromising the accuracy of SAR calculation. It is found that the Spline interpolation method helps in the reduction of MRI scan time and fast estimation of the SAR

A fast interpolation approach for the calculation of permittivity and conductivity to estimate the SAR

Thermal effects on the dynamical hysteresis in VCSEL turn-on and turn-off has been studied experimentally and theoretically. Both normal hysteresis and negative hysteresis are observed in VCSEL turn-on and turn-off.

S. Priyadarshi

Papers

Experimental Investigations of Time-Delay Signature Concealment in Chaotic External Cavity VCSELs Subject to Variable Optical Polarization Angle of Feedback

Thermal effects and dynamical hysteresis in the turn-on and turn-off of vertical-cavity surface-emitting lasers

Optimal operating conditions for external cavity semiconductor laser optical chaos communication system

A fast interpolation approach for the calculation of permittivity and conductivity to estimate the SAR

Experimental and theoretical study of thermal effects on the dynamical hysteresis in VCSEL turn-on and turn -off